Money, Intermediation, and Banking, Policy Discussion Paper 2008-1

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Money Intermediation and Banking David Andolfattoy Ed Nosalz Abstract The business of money creation is conceptually distinct from that of intermediation Yet these two activities are frequently but not always combined together in the form of a banking system We develop a simple model to examine the question When is banking essential There is a role for money due to a lack of record keeping and a role for intermediation due to the existence of private information both money and intermediation are essential When monitoring costs associated with intermediation are su ciently low the two activities can be separated from one another However when monitoring costs are su ciently high a banking system that combines these two activities is essential JEL Codes E42 G21 Keywords money intermediation banking We would like to thank a referee for extremely perceptive and helpful comments and observations as well as John Chant David Laidler Peter Rupert Shouyong Shi Bruce Smith Nurlan Turdaliev Steve Williamson and Randy Wright for their comments on earlier drafts of this paper We are grateful for the comments received on our presentations of this work at Hitotsubashi University Tokyo the Institute for Advanced Studies Vienna the Institute for Monetary and Economic Studies Bank of Japan the Canadian Macro Study Group Philadelphia Fed University of Pennsylvania Monetary Economics Conference and the Cleveland Fed Payments and Banking Workshop This research was funded in part by Social Sciences and Humanities Research Council of Canada The views expressed here do not necessarily re those of the Federal Reserve Bank of Chicago or ect of the Board of Governors of the Federal Reserve System y Department of Economics Simon Fraser University Burnaby British Columbia Canada V5A 1S6 and Rimini Centre for Economic Analysis email dandolfa sfu ca z Federal Reserve Bank of Chicago 230 South LaSalle Street Chicago IL email ed nosal chi frb org 1 1 Introduction We view a banking system as an institutional structure that combines two primary activities liquidity provision and intermediation We de ne liquidity provision as the supply of payments instruments and intermediation as the pooling monitoring and transformation of individual securities into alternative debt instruments These two activities are conceptually distinct a point highlighted by Friedman 1960 among others In both theory and practice liquidity provision can occur in the absence of intermediation and intermediation can occur in the absence of liquidity provision Nevertheless we frequently observe these two activities combined within agencies that are commonly called banks or institutional structures known as banking systems That is banks are unique among intermediated structures in that their liabilities are designed to be money To the best of our knowledge we are unaware of any theory that explains why banking the way in which we de ne it here might be essential 1 There is of course a large literature on the theory of banking But for most of this literature the term bank can be replaced with intermediary For example Diamond and Dybvig 1983 explain the emergence of intermediated structures But as the liabilities of their intermediaries do not circulate they do not t our de nition of a bank In Cavalcanti and Wallace 1999 banks issue money that circulates in the economy but they are not intermediaries Berentsen Camera and Waller 2007 examine a monetary economy in which a bank accepts deposits of cash and issues liabilities against cash reserves However in their model too bank liabilities do not circulate Similarly in Smith 2003 banks are indistinguishable from say insurance companies as their liabilities do not circulate in any meaningful sense Cavalcanti Erosa and Temzelides examine models in which a subset of private agents issue liabilities backed by reserves of cash held at a clearinghouse These agents resemble banks in that they accept cash deposits and issue liabilities that circulate But their banks are not intermediaries and hence do not t our de nition of a bank The same observation applies to the banks studied in He Huang and Wright 2005 Naturally our review of the literature above should not be construed as 1 By banking being essential we mean that more desirable allocations can be achieved if the activities of liquidity provision and intermediation are performed jointly by one agency relative to having each service supplied by separate entities 2 criticism as most of these papers do not focus on the question of whether a banking system is essential To address the question that concerns us here we take the following approach First we ignore any meaningful role for at money While at money plays an important role in modern economies and arguably in highly primitive ones it seems clear that the development of banking and private money preceded the widespread use of governmentissued at money Hicks 1989 Instead we adopt a simple nite horizon model similar to Kiyotaki and Moore 2002 to introduce the need for a circulating medium Moreover to distinguish the business of banking from insurance we abstract from insurance motives entirely by assuming riskneutral agents Intermediation in our model is instead motivated by the need for a delegated monitor along the lines of Diamond 1984 and Williamson 1986 Our model emphasizes two key frictions both of which feature prominently in the literatures on money and intermediation The rst friction is the absence of a public access record keeping technology The second friction is private information over the returns that are realized across individual investment projects In the absence of either friction the economy functions perfectly well without anything that one might label as money or as a banking system Absent a record keeping device a tangible medium of exchange is essential When private information is introduced and monitoring is costly an intermediated structure a delegated monitor is essential It is not however entirely obvious why the services of liquidity provision and intermediation should be performed by the same agent or agency Our main result is that even when money and intermediation are both essential banking is inessential when monitoring costs are su ciently small However a banking system is essential when monitoring costs are su ciently large 2 The Benchmark Environment There are three dates three time dated goods and three types of agents all labeled i There are N agents of each type where N 1 is a nite integer A type i agent prefers good i to good i 1 modulo 3 but receives no bene t from consuming good i 1 modulo 3 2 Preferences are linear 2 In what follows we will suppress the modulo 3 quali cation 3 and given by ci ci 1 where ci represents good i consumption and Output is divisible and nonstorable A type i agent produces good i 1 at date i 1 Production outcomes are random at the individual level where agent i output realization success or failure is revealed at date i 1 s There is no aggregate uncertainty In particular at each date F agents fail to produce output where 0 F N From an individual perspective F N represents the probability of failing to produce output In the event of success an agent produces y 0 units of output Since there is no aggregate uncertainty total output at each date is given by 1 N y where F N Throughout we assume that type 1 agents have a commitment technology and that all other agents types do not In the benchmark environment we assume that individual outputs are observable and that there is a publicaccess record keeping device Later on we modify this environment by rst removing the public assess record keeping device and then by assuming that individual outputs are private information When output is assumed to be private information in section 5 we will introduce a monitoring technology 3 The Ex Ante E cient Allocation Given our simple setup the ex ante e cient allocation should be obvious Since type i agents value date i goods more than their own a planner would allocate all date i output 1 N y to type i agents Because agents are risk neutral each type i agent is indi erent between mechanisms that in expectation deliver 1 y units of good i to him Hence an ex ante e cient allocation allows each agent to achieve an ex ante utility payo equal to 1 y The implementation scheme described below builds on the fact that 1 type 1 agents can commit 2 output is observable and 3 that there is a public access record keeping device There are potentially many ways to implement the e cient allocation Here is one The allocation of good i is given by the following simple rule the total amount of output surrendered to 4 a mechanism3 at date 1 is equally divided among all type 1 agents the total output surrendered to the mechanism at dates 2 and 3 is divided among the type 2 and type 3 agents respectively in proportion to output surrendered at dates 1 and 2 Agents play the following strategies type 2 and type 3 agents surrender their output if they have it at dates 1 and 2 respectively and type 1 agents promise to surrender their output if they have it at date 3 It is easy to see that the above allocation rule and strategies constitute an equilibrium If all other agents play the proposed strategies a type 2 or type 3 agent who defects by consuming his own output receives a payo of y which is less than the equilibrium payo of y And since type 1 agents can commit they will surrender their output at date 3 4 Lack of Record Keeping The allocation rule and strategies described above are infeasible if a publicaccess record keeping device does not exist since they rely on some form of public memory For trade to occur some sort of physical and noncounterfeitable object is needed Kocherlakota 1998 Standard monetary models feature an in nite horizon a complete lack of record keeping and no commitment In these environments trade is facilitated by objects that are at in nature such as intrinsically useless and unbacked tokens In contrast our environment has a nite horizon with some limited commitment in the form of type 1 agents ability to commit Here monetary exchange can work o the fact that a subset of agents can commit to redeem tokens As we shall see below whether these tokens are created by society and endowed to type 1 agents or whether type 1 agents create tokens on their own is irrelevant in terms of implementable allocations All that is necessary is that some monetary object exist Imagine then that each type 1 agent is endowed with a divisible durable and non counterfeitable token Consider the following allocation rules and strategies The allocation rule for output is similar to that described above the total amount of output surrendered to the mechanism at date i is divided 3 A mechanism simply accepts and distributes output and possibility other objects according to a prescribed rule 5 among the type i agents in proportion to the amount of tokens they surrender The allocation rule for tokens is at date i the total amount of tokens surrendered to the mechanism is divided among the type i 1 agents in proportion to the output they surrendered Agents play the following strategies The strategy for tokens is type i agents surrender tokens at date i if they have them The strategies for output are identical to the record keeping environment type 2 and and type 3 agents surrender their output if they have it at dates 1 and 2 respectively and type 1 agents promise to surrender their output if they have it at date 3 The allocation rules and strategies have been constructed in a way that makes it transparent that in equilibrium the supply of tokens serves as a perfect substitute for the missing public access record keeping device In particular if any type 2 or type 3 agent consumes his output then he will be unable to consume any of the date 2 or date 3 goods respectively Before we proceed some brief remarks on the at like nature of money are in order While the tokens in the equilibrium described above do not have any explicit backing they are not really pure at instruments since type 1 agents commit to accept them as payment for their output In this sense tokens are de facto backed by some commitment power Therefore instead of endowing agents with tokens we could alternatively assume that type 1 agents create them with an explicit promise of to redeem them for output in the future if they have it and then use the above strategies and allocation rules to implement an ex ante e cient allocation 4 Under this interpretation 4 From a date 3 perspective tokens issued by type 1 agents will be heterogenous some tokens are worth y those issued by successful type 1 agents and while others are worthless those issued by unsuccessful type 1 agents But given the allocation rules for tokens and goods described above the mechanism treats all type 1 money symmetrically We assume that agents surrendered their tokens before the output realizations are observed Implicitly one can interpret the symmetric treatment of date 1 tokens as a form of intermediation For example suppose that at the beginning of date 3 all type 3 agents holding tokens which are claims issued by type 1 agents collectively pool them and issue new claims or tokens against them that give the holder proportional share of total output this is done prior to the revelation of the type 1 agents date 3 output realizations Type 3 agents surrender output to the mechanism type 3 agents collectively surrender the tokens issued by type 1 agents and the mechanism distributes output in proportion to the type 3 tokens surrendered by type 3 agents The act of the type 3 agents pooling the tokens issued by type 1 agents and then re issuing new riskless tokens is the form of intermediation envisioned by Diamond 1984 and Williamson 1986 Note however that there is nothing fundamental about having a set of the type 3 agents acting as the 6 tokens look a lot like inside money 5 5 Private Information We now assume that each agent production outcome is private information s and that type 1 agents can commit only to what is publicly observable 6 In this situation the strategies and allocation rules described in the previous section no longer constitute an equilibrium In particular type 1 agents will always have an incentive to that claim their output is zero since output is not publicly observable and those who actually produce y will consume it Without any further modi cations to the environment the only equilibrium is autarky Following Townsend 1979 and Williamson 1986 we introduce a costly monitoring technology The technology works as follows If a producing agent fails to surrender his output then the actual level of production 0 or y can be revealed if he is monitored The cost of monitoring a producing agent is 0 utils The monitoring cost can be shared or spread out over any number of agents If for example M agents each expend M utils then their combined e ort allows them to monitor one producing agent Individual monitoring costs as well as the monitoring outcome are observable It turns out that monitoring is relevant only at date 3 and that only type 1 and type 3 agents would ever have an incentive to monitor 7 Type 3 agents may have an incentive to monitor because in any equilibrium with trade they are holding tokens or inside money that can be used to purchase the output they value Note that because type 3 agents have no commitment intermediary in principle type 1 or type 2 agents may also perform this task 5 The notion of inside money here is similar to that in Cavalanti and Wallace 1999 In Cavalcanti and Wallace 1999 agents who are monitored can issue money In our setup we can re interpret type 1 agents as being monitored and assume that there exists a court that enforces contracts on the based on observables Furthermore since type 2 and type 3 agents are not monitored they are not subject to the enforcement mechanism 6 If type 1 agents were able to commit unconditionally then the introduction of private information has no e ect on equilibrium outcomes The assumption that type 1 agents can only commit to what is observable is standard in the literature e g Townsend 1979 and Williamson A type 2 agent would never monitor at date 3 since he does not value date 3 output and cannot commit to monitoring 7 power their decision to monitor must be sequentially rational In contrast since type 1 agents can commitment their decision to monitor themselves need not respect sequential rationality We will de ne an intermediary as a set of agents who collectively perform the task of monitoring 8 Since type 2 agents do not have an incentive to monitor they cannot be an intermediary 5 1 Type 3 Intermediation In this section we consider strategies that can be interpreted as giving rise to an institutional structure that separates money issue and intermediation More speci cally we assume that type 1 agents are responsible for creating the economy monetary instrument and type 3 agents are collectively s responsible for intermediation In terms of the timing of events for type 3 intermediation we assume that the decision to monitor or not is made after date 3 output is surrendered by type 1 agents and distributed to type 3 agents This timing serves to emphasize the fact that type 3 agents cannot commit to future actions Consider the following equilibrium strategies and allocation rules most of which are identical to those described in the previous section The allocation rule for goods at date i is to divide the total amount of goods surrendered to the mechanism at date i among the type i agents in proportion to the amount of tokens they surrendered The allocation rule for tokens divides the total amount of tokens surrendered to the mechanism at date i among the type i 1 agents in proportion to the amount of output surrendered at date i The strategies for goods for type i agents to surrender output if they have it In addition i at date 1 each type 1 agent creates a token that is redeemable for y units of date 3 output if he has it and ii successful 8 In footnote 4 we motivated the symmetric treatment of tokens issued by type 1 agents at date 3 as a form of intermediation Continuing this line of discussion in an environment characterized by asymmetric information if a group of agents transforms risky tokens issued by type 1 agents into riskless ones at date 3 they must also be willing to perform or at least manage the task of monitoring in the event that total output surrendered falls short of 1 N y So the set of agents that are involved in transforming claims are also the set of agents who must manage monitoring Since without loss of generality we assume that the mechanism treats all date 1 issued claims symmetrically the set of agents who do the monitoring is the intermediary 8 type 3 producers who surrender tokens at date 3 monitor all type 1 agents who did not surrender output at date 3 if total date 3 output surrendered is less than N F y otherwise they do not monitor anyone The interesting questions to examine here are 1 will successful type1 producers surrender their output at date 3 and 2 will type 3 agents monitor if total date 3 output falls below N F y Since we are interested in implementing a truth telling equilibrium let us suppose that all successful type 1 agents surrender their output at date 3 and then examine whether conditional on this behavior any individual type 1 agent has an incentive to withhold his output Note that such a deviation will be pro table if there is even the smallest chance that the deviating type 1 agent escapes monitoring Therefore any equilibrium requires that if total output is less than N F y then any agent who does not surrender output is monitored with probability one 9 Suppose then that a successful type 1 agent does not surrender his output at date 3 The above strategies imply that type 3 agents with tokens will monitor all of the F 1 type 1 agents who did not surrender output In this case the cost of monitoring is F 1 N F utils for each type 3 agent who monitors This monitoring activity will recover y units of the hidden output Whether type 1 agents have an incentive to surrender output depends on whether the delegated monitors nds it sequentially rational to monitor in m the event of a defection Let U3 denote the expected payo to monitoring n and U3 denote the expected payo to not monitoring Then F 1 N F m U3 y and n U3 N F N 1 F y m Hence type 3 agents will decide to monitor if U3 and only if y F N n m U3 and U3 n U3 if Implicitly we assume that sequential monitoring of type 1 agents is not possible Allowing for this changes a bit of the arithmetic but not our main conclusions 9 This inequality is obviously satis ed if 0 but in general we can de ne a reservation monitoring cost such that y N 1 or y N We can conclude that monitoring by type 3 agents with money will be sequentially rational for any Hence if is su ciently small in this sense then conditional on all other successful type 1 producing agents surrendering their output a successful type 1 producing agent will not have an incentive to hide his output In other words the ex ante e cient allocation can be implemented under an institutional arrangement that separates the businesses of the money issue from intermediation Hence a banking arrangement is not essential If however then the ex ante e cient allocation cannot be implemented under such an arrangement 5 2 Type 1 Intermediation Banking Since type 1 agents can commit the monitoring intermediation function can simply be delegated collectively to them That is when the type 1 agents create their tokens or liabilities at date 1 they also commit to monitoring all type 1 agents who do not surrender output at date 3 in the event that aggregate output falls short of N F y Since this threat of monitoring is credible no type 1 agent has an incentive to hide output at date 3 any hidden output will ultimately be discovered and con scated Hence in equilibrium no monitoring will occur and the ex ante e cient allocation can be implementable regardless of the size of In the stark environment that we consider a banking arrangement weakly dominates an institutional arrangement that separates the businesses of moneyissue and intermediation over the entire parameter space and strictly dominates for parameter con gurations y N that satisfy y N 1 It is in these latter cases that we say that banking is essential It is interesting to note that is a decreasing function of N see 1 It is tempting to interpret N as a measure of population size If this is the case 10 Suppose only a subset of type 3 agents with tokens decide to monitor after they observe the amount the amount of output is N F 1 y Owing to the linearity of preferences the condition for monitoring for any subset of the type 3 agents with tokens is also given by condition then the model has a nice implication that banking arrangements are likely to be more prevalent in larger economies ceteris paribus of course The model also suggests that banking arrangements are likely to be more prevalent in environments where monitoring costs are high and or the probability of failure is high relative to the return to investment The parameter re ects the di culty of acquiring information say in a bankruptcy proceeding and there is some reason to believe that this parameter may increase over time as economic relationships and accounting practices grow in complexity 6 Discussion Our model is able to capture some but certainly not all aspects of the development of money and banking in history First our model is consistent with the idea that anyone with a capacity to issue money will endeavor to do so to meet the demand for liquidity Absent legal restrictions prohibiting the practice of small note issue this type of behavior is prevalent throughout recent history For example Bodenhorn 1993 quotes an Italian General Secretary of the Banco D Italia how prior to everyone was issuing notes even individuals and commercial rms the country was overrun with little notes of 50 25 and 20 centimes issued by everyone who liked to do so The author also notes that when state legislation banned U S banks from issuing notes of less than 5 railroad companies public houses merchants and even churches lled the void with their own notes Even Adam Smith 1937 pp noted with some disapproval one might add how small notes drove specie from the country One aspect of history that our model cannot account for is the widespread regulatory e orts that were expended to prohibit private small note issue One common argument was that holders of a few small notes had little incentive to expend real resources on monitoring or determining authenticity Even those holding large quantities of notes may have had little incentive to monitor since others might have incentive to free ride on their e orts But as Bodenhorn 1993 pg 822 reports in antebellum America at least independent businessmen known as note brokers made markets in banknotes at the same time providing information and monitoring services This institutional setup bears some resemblance to the one that emerges in our model where money issue is separated from monitoring 11 What then of the emergence of banking arrangements The interpretation that we o er here is not with respect to the emergence of agencies often referred to as banks per se but rather the emergence of what one might call a banking system broadly de ned to include regulatory agencies As noted by Klein 1974 many early U S banks became members of private certifying and monitoring agencies which performed some of the functions similar to modern central banks A famous example is the Su olk banking system e g see Smith and Weber 1999 In an interesting paper Gorton and Mullineaux 1987 argue that the capacity of private note brokers to monitor and control the behavior of bank managers was increasingly eroded as demand deposits came to supplant bank notes during the nineteenth century While our model is not rich enough to distinguish between bank notes and demand deposits this historical development can be thought of manifesting itself as an increase in our model parameter and hence an increase in the likelihood of the emergence of banking 7 Conclusion We describe an environment where absent record keeping money is essential Whether this money takes the form of a at token or of an explicitly backed private liability is indeterminate although we do argue that a at token in conjunction with type 1 agents promises to surrender output amounts to inside money Either way however a speci c subset of agents must initially be in possession of the monetary instrument whether it is endowed to them or whether they create it themselves is irrelevant When the environment is further modi ed by assuming that idiosyncratic production shocks are private information and that such information can only be revealed through costly monitoring some form of intermediation is essential This is to say that it becomes essential for some group of agents to agree collectively monitor the issuers of some pool of securities But it is not obvious if it matters who these agents are If monitoring costs are su ciently small in the sense that then the monitoring function can be delegated either to those who issue the money or to those who are ultimately in a position to redeem it On the other hand if monitoring costs are su ciently high in the sense that then it is essential that the monitoring function is delegated to those agents responsible for creating the 12 economy monetary instrument s While our model is very simple it arguably allows us to interpret some aspects of the development of money and banking in recent history As such the basic ideas embedded within the model may serve to develop a richer class of models designed to explain more complicated aspects of the way 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